[機統] Poisson和條件機率應用問題
各位大大們好，初次來到本版，若有冒犯請多多包含
本人之前大多修電機相關課程，直到這學期才選修到數學性較重的機率，目前做到一些
題目感到有疑惑，懇請大大們指點一下:
Poisson-
SSI chips, essential to the running of a computer system, fail in
accordance with a Poisson distribution with the rate of one chip
in about five weeks. If there are two spare chips on hand, and if
a new supply will arrive in eight weeks, what is the probability
that during the next eight weeks the system will be down for a
week or more, owing to a lack of chips?
這題很明顯就是用Poisson的equation。但不知道是要帶入什麼數值進去，而且出來的答案
好像還要再經過一些加工才能算正確解答...?
條件機率-
A father asks his son to cut their backyard lawn.Since he does not
specify which of three sons is to do the job, each boy tosses a coin to
determine the odd person, who must then cut the lawn. In the case that
all three gets heads or tails, they continue until reach a decision.
Let p be the probability of heads and q = 1-p, the probability of
tails.
(a) Find the probability that they reach a decison in less than n
tosses.
(b) If p = 1/2, what is the minimum number of tosses required to reach
a decision with probability 0.95.
這題也是一看知道要用P(E)=pP(E|H)+qP(E|T)這類等式，但P(E|H)和P(E|T)要怎麼表示
就不知道了...
另外這題不知道歸類在哪裡(完全無頭緒><)，如果可以的話大大們能順便提示一下嗎?
謝謝大家幫忙>///<
A contestant on a quiz show is presented with two questions,
question 1 and question 2, which he is to attempt to answer in
some order chosen by him. If he decides to try question i, i=1, 2
first, then he will be allowed to go on to question j, j≠i only if
his answer to is correct. If his initial answer is incorrect, he is
not allowed to answer the other question. The contestant is to
receive Vi dollars if he answers question I correctly, I=1,2.
Thus, for instance, he will receive V1+V2 dollars if both
questions are correctly answered. If the probability that he
knows the question I is Pi, i = 1, 2, which question should he
attempt first so as to maximize his expected winnings? Assume
that the events Ei, i=1,2, that he knows the answer to question I,
are independent events.
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